Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder

Abstract

We study coherent wave scattering through waveguides with a step-like surface disorder and find distinct enhancements in the reflection coefficients at welldefined resonance values. Based on detailed numerical and analytical calculations, we can unambiguously identify the origin of these reflection resonances to be higher-order correlations in the surface disorder profile which are typically neglected in similar studies of the same system. A remarkable feature of this new effect is that it relies on the longitudinal correlations in the step profile, although individual step heights are random and thus completely uncorrelated. The corresponding resonances are very pronounced and robust with respect to ensemble averaging, and lead to an enhancement of wave reflection by more than one order of magnitude.The problem of scattering off a rough surface is a central topic in physics which occurs for many different types of waves and on considerably different length scales [1][2][3][4]. Phenomena induced by surface corrugations play a major role in the study of acoustic, electromagnetic, and matter waves alike and appear in macroscopic domains such as acoustic oceanography and atmospheric sciences [5,6], but also emerge on much smaller length scales, e.g., for photonic crystals [7], optical fibers and waveguides [8,9], surface plasmon polaritons [10], metamaterials [11], thin metallic films [12-14], layered structures [15], graphene nanoribbons [16,17], nanowires [18][19][20], and confined quantum systems [21,22]. While having a detrimental effect on the performance of many of the above systems, surface roughness can also be put to use, e.g., for the fabrication of high-performance thermoelectric devices [23,24] and for light trapping in silicon solar cells [25]; rough surfaces cause anomalously large persistent currents in metallic rings [26] and provide the necessary scattering potential to manipulate ultra-cold neutrons which are bound by the earthʼs gravity potential [27].In view of this sizeable research effort, it might come as a surprise that even quite fundamental effects emerging in surface-disordered systems are still not fully understood. Consider here, in particular, the problem of wave transmission through a surface-corrugated guiding system which we will study in the following. As demonstrated in detail below, even a very elementary and well-studied model system, consisting of a two-dimensional (2D) waveguide with a step-like surface disorder on either boundary (see figure 1), can only be inadequately described with conventional techniques. The reason why the knowledge on surface-disordered waveguides is still far behind the state of the art for bulk-disordered systems is mainly because of the difficulties arising from the non-homogeneous character of transport via different propagating modes (channels). As was numerically shown in [28], the transmission through multi-mode waveguides depends on many characteristic length scales which are specific for each mode. As a result, one can observe a coexistence of b...

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Coupled-mode approach to square-gradient Bragg-reflection resonances in corrugated dielectric waveguides

“…In Fig. 2 a) and b) the calculated reflectivity R and the transmission T , respectively, are displayed as a function of (vacuum) wave vector k. Two sharp peaks caused by Bragg scattering into the same mode R 13 occur as expected at twice the value of β. From this calculations it is apparent that square gradient Bragg scattering is as strong as Bragg scattering.…”

“…The peak is clearly visible, but overestimated by the theory. For inter-mode scattering R (b) 13 and R (sg) 13 , the situation is re- versed. The reflection resonance is much stronger than predicted by the theory, for both scattering mechanisms.…”

“…First, our result is valid for any boundary and the reflectivity is directly calculated from the boundary in a straightforward way. A cumbersome generation procedure to generate random boundaries that comply with the statistical requirements of the statistical approach (see [12,13]) are not necessary. Second, the derivation does not depend on the type of boundary.…”